4.5b Standing Waves: Calculations

THE IB SAYS

Essential idea: When travelling waves meet they can superpose to form standing waves in which energy may not be transferred.

Understandings: The nature of standing waves; Boundary conditions; Nodes and antinodes

Applications and skills: Describing the nature and formation of standing waves in terms of superposition; Distinguishing between standing and travelling waves; Observing, sketching and interpreting standing wave patterns in strings and pipes; Solving problems involving the frequency of a harmonic, length of the standing wave and the speed of the wave

Guidance: Students will be expected to consider the formation of standing waves from the superposition of no more than two waves; Boundary conditions for strings are: two fixed boundaries; fixed and free boundary; two free boundaries; Boundary conditions for pipes are: two closed boundaries; closed and open boundary; two open boundaries; For standing waves in air, explanations will not be required in terms of pressure nodes and pressure antinodes; The lowest frequency mode of a standing wave is known as the first harmonic; The terms fundamental and overtone will not be used in examination questions

Data booklet: v = fλ

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Harmonics

When standing waves are created in an oscillator, such as a string or a pipe, the two most common examples you will see in IB DP Physics, they will only occur for certain frequencies. The lowest frequency at which the longest wavelength standing wave will be created is called the first harmonic. The value of that frequency depends on the speed of the wave in that medium, the length of the oscillator, and the boundary conditions (is there a node or an antinode at the ends of the oscillator).

String (node at each end)

This is a common example, and is applicable to many stringed musical instruments amongst other applications.

Pipe (node at one end, anti-node at the other)

This example is also common and is applicable to the majority of wind instruments.

Additional videos

Resources from textbooks

Oxford Physics: pages 160 - 162

Hamper HL (2014): pages 168 - 169 / 179 - 181

Relevant questions from Dot Point Physics (11 Wave phenomena)

pages 81-89 - NB: This used to be a HL topic so is in the HL book.